YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [tt] = 1, [u] = 6, [isQid](x0) = x0, [active](x0) = x0, [nil] = 1, [and](x0, x1) = x0 + x1, [isPal](x0) = 3x0, [__](x0, x1) = 2x0 + x1 + 4, [isNeList](x0) = 2x0, [o] = 2, [e] = 1, [a] = 4, [isNePal](x0) = 2x0, [i] = 6, [isList](x0) = 2x0 + 2, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z + 12 >= 2X + 2Y + Z + 8 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2X + 5 >= X = mark(X) active(__(nil(),X)) = X + 6 >= X = mark(X) active(and(tt(),X)) = X + 1 >= X = mark(X) active(isList(V)) = 2V + 2 >= 2V = mark(isNeList(V)) active(isList(nil())) = 4 >= 1 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + 2V2 + 10 >= 2V1 + 2V2 + 4 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 2V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 4V1 + 2V2 + 8 >= 2V1 + 2V2 + 2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 4V1 + 2V2 + 8 >= 2V1 + 2V2 + 2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 2V >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 6I + 4P + 16 >= I + 3P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 3V >= 2V = mark(isNePal(V)) active(isPal(nil())) = 3 >= 1 = mark(tt()) active(isQid(a())) = 4 >= 1 = mark(tt()) active(isQid(e())) = 1 >= 1 = mark(tt()) active(isQid(i())) = 6 >= 1 = mark(tt()) active(isQid(o())) = 2 >= 1 = mark(tt()) active(isQid(u())) = 6 >= 1 = mark(tt()) mark(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = active(and(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(isList(X)) = 2X + 2 >= 2X + 2 = active(isList(X)) mark(isNeList(X)) = 2X >= 2X = active(isNeList(X)) mark(isQid(X)) = X >= X = active(isQid(X)) mark(isNePal(X)) = 2X >= 2X = active(isNePal(X)) mark(isPal(X)) = 3X >= 3X = active(isPal(X)) mark(a()) = 4 >= 4 = active(a()) mark(e()) = 1 >= 1 = active(e()) mark(i()) = 6 >= 6 = active(i()) mark(o()) = 2 >= 2 = active(o()) mark(u()) = 6 >= 6 = active(u()) __(mark(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2) __(X1,mark(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2) __(active(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2) __(X1,active(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,X2) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) and(active(X1),X2) = X1 + X2 >= X1 + X2 = and(X1,X2) and(X1,active(X2)) = X1 + X2 >= X1 + X2 = and(X1,X2) isList(mark(X)) = 2X + 2 >= 2X + 2 = isList(X) isList(active(X)) = 2X + 2 >= 2X + 2 = isList(X) isNeList(mark(X)) = 2X >= 2X = isNeList(X) isNeList(active(X)) = 2X >= 2X = isNeList(X) isQid(mark(X)) = X >= X = isQid(X) isQid(active(X)) = X >= X = isQid(X) isNePal(mark(X)) = 2X >= 2X = isNePal(X) isNePal(active(X)) = 2X >= 2X = isNePal(X) isPal(mark(X)) = 3X >= 3X = isPal(X) isPal(active(X)) = 3X >= 3X = isPal(X) problem: active(isNeList(V)) -> mark(isQid(V)) active(isNePal(V)) -> mark(isQid(V)) active(isPal(V)) -> mark(isNePal(V)) active(isQid(e())) -> mark(tt()) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [0] [u] = [0] [0], [1 0 0] [1] [isQid](x0) = [0 0 0]x0 + [0] [1 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [nil] = [0] [0], [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [o] = [0] [0], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [1] [isNePal](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [0] [i] = [0] [0], [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [1] orientation: [1 0 0] [1] [1 0 0] [1] active(isNeList(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isQid(V)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] active(isNePal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isQid(V)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] active(isPal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isNePal(V)) [0 0 0] [1] [0 0 0] [1] [1] [0] active(isQid(e())) = [0] >= [0] = mark(tt()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [1] [1] [1 0 0] [0] [1 0 0] [0] mark(isList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNeList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNeList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isQid(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isQid(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNePal(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isPal(X)) [0 0 0] [1] [0 0 0] [1] [0] [0] mark(a()) = [0] >= [0] = active(a()) [1] [1] [0] [0] mark(e()) = [0] >= [0] = active(e()) [1] [1] [0] [0] mark(i()) = [0] >= [0] = active(i()) [1] [1] [0] [0] mark(o()) = [0] >= [0] = active(o()) [1] [1] [0] [0] mark(u()) = [0] >= [0] = active(u()) [1] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isList(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isList(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNeList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNeList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isQid(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isQid(X) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1] [1 0 0] [1] isQid(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isQid(X) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNePal(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNePal(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isPal(X) [0 0 0] [0] [0 0 0] [0] problem: active(isNeList(V)) -> mark(isQid(V)) active(isNePal(V)) -> mark(isQid(V)) active(isPal(V)) -> mark(isNePal(V)) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) mark(o()) -> active(o()) mark(u()) -> active(u()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [0] [u] = [0] [1], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 1 1] , [0] [nil] = [0] [0], [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [0], [1 0 0] [1] [isPal](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [1 0 0] [1] [isNeList](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [0] [o] = [0] [1], [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [1] [isNePal](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [0] [i] = [0] [0], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 0]x0 [1 0 1] orientation: [1 0 0] [1] [1 0 0] active(isNeList(V)) = [0 0 0]V + [0] >= [0 0 0]V = mark(isQid(V)) [1 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] active(isNePal(V)) = [0 0 0]V + [0] >= [0 0 0]V = mark(isQid(V)) [1 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1] active(isPal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isNePal(V)) [1 0 0] [1] [1 0 0] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(__(mark(X1),mark(X2))) [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(and(mark(X1),X2)) [1 0 1] [1 0 0] [1] [1 0 1] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 0] [1 0 0] mark(isList(X)) = [0 0 0]X >= [0 0 0]X = active(isList(X)) [1 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isNeList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNeList(X)) [1 0 0] [1] [1 0 0] [0] [1 0 0] [1 0 0] mark(isQid(X)) = [0 0 0]X >= [0 0 0]X = active(isQid(X)) [1 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNePal(X)) [1 0 0] [1] [1 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isPal(X)) [1 0 0] [1] [1 0 0] [1] [0] [0] mark(a()) = [0] >= [0] = active(a()) [0] [0] [0] [0] mark(e()) = [0] >= [0] = active(e()) [0] [0] [0] [0] mark(i()) = [0] >= [0] = active(i()) [0] [0] [1] [0] mark(o()) = [0] >= [0] = active(o()) [1] [1] [1] [0] mark(u()) = [0] >= [0] = active(u()) [1] [1] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [1 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 1] [1 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 1 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 1] [0 1 1] [1] [0 0 1] [0 0 1] [1] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [1 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [1 0 0] isList(mark(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isList(active(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [1] isNeList(mark(X)) = [1 0 1]X + [0] >= [1 0 0]X + [0] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNeList(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isNeList(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] isQid(mark(X)) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isQid(active(X)) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [1] isNePal(mark(X)) = [1 0 1]X + [0] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNePal(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isPal(mark(X)) = [1 0 1]X + [1] >= [1 0 0]X + [1] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(active(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = isPal(X) [0 0 0] [0] [0 0 0] [0] problem: active(isPal(V)) -> mark(isNePal(V)) mark(nil()) -> active(nil()) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isQid(X)) -> active(isQid(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(isPal(X)) -> active(isPal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [1 1 1] [0], [1 0 0] [active](x0) = [0 0 1]x0 [0 1 0] , [0] [nil] = [1] [0], [1 1 1] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [isPal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [1 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [0] [i] = [0] [0], [1 0 0] [1] [isList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [0] [mark](x0) = [0 0 1]x0 + [0] [0 0 0] [1] orientation: [1 0 0] [0] [1 0 0] [0] active(isPal(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isNePal(V)) [0 0 0] [1] [0 0 0] [1] [1] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [1] [0] [1 0 0] [1] [1 0 0] [1] mark(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(isList(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] mark(isNeList(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(isNeList(X)) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [0] mark(isQid(X)) = [1 1 1]X + [0] >= [1 1 1]X + [0] = active(isQid(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(isNePal(X)) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [0] mark(isPal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isPal(X)) [0 0 0] [1] [0 0 0] [1] [0] [0] mark(a()) = [0] >= [0] = active(a()) [1] [0] [0] [0] mark(e()) = [0] >= [0] = active(e()) [1] [0] [0] [0] mark(i()) = [0] >= [0] = active(i()) [1] [0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [1 1 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [1 1 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = __(X1,X2) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 0] [0] [1 1 1] [1 0 0] [0] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 1 1] [1 0 0] [0] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 1 1] [1 0 0] [0] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] isList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] isList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isList(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 0 0] isNeList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(active(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 1 0] [0] [1 0 0] [0] isQid(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [1 1 1] [1] [1 1 1] [0] [1 0 0] [0] [1 0 0] [0] isQid(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [1 1 1] [0] [1 1 1] [0] [1 1 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(active(X)) = [0 0 0]X >= [0 0 0]X = isNePal(X) [0 0 0] [0 0 0] [1 1 0] [0] [1 0 0] [0] isPal(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isPal(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isPal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isPal(X) [0 0 0] [0] [0 0 0] [0] problem: active(isPal(V)) -> mark(isNePal(V)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 1] [0 1 0] [1], [1 0 0] [1] [isPal](x0) = [1 0 0]x0 + [0] [0 1 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] , [0] [e] = [0] [0], [0] [a] = [0] [0], [1 0 0] [isNePal](x0) = [0 1 0]x0 [0 0 0] , [0] [i] = [0] [0], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [1 1 1]x0 [0 0 0] orientation: [1 0 0] [1] [1 0 0] active(isPal(V)) = [1 1 0]V + [0] >= [1 1 0]V = mark(isNePal(V)) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 0] [1] [1 0 1] [1 0 0] [0] mark(and(X1,X2)) = [1 1 1]X1 + [1 1 0]X2 + [1] >= [1 1 1]X1 + [0 1 0]X2 + [1] = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 0] [1 0 0] mark(isList(X)) = [1 0 0]X >= [0 0 0]X = active(isList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNeList(X)) = [1 0 0]X >= [0 0 0]X = active(isNeList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNePal(X)) = [1 1 0]X >= [0 1 0]X = active(isNePal(X)) [0 0 0] [0 0 0] [0] [0] mark(a()) = [0] >= [0] = active(a()) [0] [0] [0] [0] mark(e()) = [0] >= [0] = active(e()) [0] [0] [0] [0] mark(i()) = [0] >= [0] = active(i()) [0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 1 1] [1 1 1] [1] [0 1 1] [0 1 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 1 1] [0 1 0] [1] [0 1 1] [0 1 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 1 1] [0 1 1] [1] [0 1 1] [0 1 0] [1] [1 0 1] [1 0 0] isList(mark(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isList(active(X)) = [0 0 0]X >= [0 0 0]X = isList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNeList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(active(X)) = [0 0 0]X >= [0 0 0]X = isNeList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isQid(mark(X)) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isQid(active(X)) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNePal(mark(X)) = [1 1 1]X >= [0 1 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNePal(active(X)) = [0 1 1]X >= [0 1 0]X = isNePal(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 0] [1] isPal(mark(X)) = [1 0 1]X + [0] >= [1 0 0]X + [0] = isPal(X) [1 1 1] [0] [0 1 0] [0] [1 0 0] [1] [1 0 0] [1] isPal(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isPal(X) [0 1 1] [0] [0 1 0] [0] problem: mark(tt()) -> active(tt()) mark(isList(X)) -> active(isList(X)) mark(isNeList(X)) -> active(isNeList(X)) mark(isNePal(X)) -> active(isNePal(X)) mark(a()) -> active(a()) mark(e()) -> active(e()) mark(i()) -> active(i()) __(mark(X1),X2) -> __(X1,X2) __(X1,mark(X2)) -> __(X1,X2) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isList(mark(X)) -> isList(X) isList(active(X)) -> isList(X) isNeList(mark(X)) -> isNeList(X) isNeList(active(X)) -> isNeList(X) isQid(mark(X)) -> isQid(X) isQid(active(X)) -> isQid(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) isPal(mark(X)) -> isPal(X) isPal(active(X)) -> isPal(X) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 6, [isQid](x0) = 4x0 + 1, [active](x0) = 2x0 + 4, [and](x0, x1) = 2x0 + x1 + 2, [isPal](x0) = 4x0, [__](x0, x1) = 2x0 + 2x1 + 1, [isNeList](x0) = x0, [e] = 0, [a] = 1, [isNePal](x0) = x0, [i] = 0, [isList](x0) = x0, [mark](x0) = 2x0 + 5 orientation: mark(tt()) = 17 >= 16 = active(tt()) mark(isList(X)) = 2X + 5 >= 2X + 4 = active(isList(X)) mark(isNeList(X)) = 2X + 5 >= 2X + 4 = active(isNeList(X)) mark(isNePal(X)) = 2X + 5 >= 2X + 4 = active(isNePal(X)) mark(a()) = 7 >= 6 = active(a()) mark(e()) = 5 >= 4 = active(e()) mark(i()) = 5 >= 4 = active(i()) __(mark(X1),X2) = 4X1 + 2X2 + 11 >= 2X1 + 2X2 + 1 = __(X1,X2) __(X1,mark(X2)) = 2X1 + 4X2 + 11 >= 2X1 + 2X2 + 1 = __(X1,X2) __(active(X1),X2) = 4X1 + 2X2 + 9 >= 2X1 + 2X2 + 1 = __(X1,X2) __(X1,active(X2)) = 2X1 + 4X2 + 9 >= 2X1 + 2X2 + 1 = __(X1,X2) and(X1,mark(X2)) = 2X1 + 2X2 + 7 >= 2X1 + X2 + 2 = and(X1,X2) and(active(X1),X2) = 4X1 + X2 + 10 >= 2X1 + X2 + 2 = and(X1,X2) and(X1,active(X2)) = 2X1 + 2X2 + 6 >= 2X1 + X2 + 2 = and(X1,X2) isList(mark(X)) = 2X + 5 >= X = isList(X) isList(active(X)) = 2X + 4 >= X = isList(X) isNeList(mark(X)) = 2X + 5 >= X = isNeList(X) isNeList(active(X)) = 2X + 4 >= X = isNeList(X) isQid(mark(X)) = 8X + 21 >= 4X + 1 = isQid(X) isQid(active(X)) = 8X + 17 >= 4X + 1 = isQid(X) isNePal(mark(X)) = 2X + 5 >= X = isNePal(X) isNePal(active(X)) = 2X + 4 >= X = isNePal(X) isPal(mark(X)) = 8X + 20 >= 4X = isPal(X) isPal(active(X)) = 8X + 16 >= 4X = isPal(X) problem: Qed